Investigating the temporal stability of phase offsets at 7T for field mapping and multi-channel phase combination.
Barbara Dymerska1, Siegfried Trattnig1, and Simon Daniel Robinson1

1High Field MR Centre, Department of Biomedical Imaging and Image-guided Therapy, Medical University of Vienna, Vienna, Austria


A common assumption for phase combination and dynamic distortion correction is that phase offsets ($$$Ф_0$$$), i.e. the phase of coil sensitivities, are temporally stable. We investigate the validity of this assumption at 7T for long measurements (40min) and large head rotations (up to 12°) made with multi-channel coils. We show that changes in separate-channel $$$Ф_{0,ch}$$$ have little effect on the combined phase images (unwarping errors of 0.2 voxel, reduction in phase matching quality by 2%). We thus conclude that the assumption of $$$Ф_0$$$ temporal stability holds and methods based on this assumption should work at 7T with substantial motion.


To assess the common assumption that phase offsets $$$(Ф_0)$$$, i.e. the phase of complex coil sensitivities, are temporally stable and to investigate the validity of this assumption at 7T for long measurements made with multi-channel coils and large head rotations.


Phase for each channel $$$Ф_{ch}$$$ consist of echo-time-independent phase offset $$$Ф_{0,ch}$$$, and a term describing local variations from the static magnetic field, ΔB0:

$$\phi_{ch}(TE)=\phi_{0,ch}+2\pi\gamma TE \triangle B_{0}$$

In order to create accurate B0 field-maps (for correction of EPI distortions) or optimally combine phase data from multi-channel coils (for SWI or QSM) one needs to remove $$$Ф_{0,ch}$$$ from the phase from each channel. Several dynamic distortion correction methods share a common assumption that $$$Ф_0$$$ is temporally stable1–4. They have only been tested for moderate motion, using volume coils and up to 3T, where $$$Ф_0$$$ varies slowly in space. At 7T with multi-channel coils and shorter RF wavelengths $$$Ф_0$$$ differs for each coil element and is more inhomogeneous, which increases its vulnerability during long acquisitions or motion (changing the coil loading). Changes in $$$Ф_0$$$ also influence the quality of phase combination, reducing SNR, in methods using a reference scan for $$$Ф_0$$$ estimation5–7. To address these concerns we examine the variations in $$$Ф_{0,ch}$$$ due to technical causes and motion and their influence on the accuracy of field-mapping and phase combination.


Measurements were carried out with a 7T Siemens scanner and a 32-channel head coil. Changes in $$$Ф_{0,ch}$$$ caused by scanner instabilities were measured in a phantom during four dual-echo EPI scans of 10 min each (TEs=[9.4,27.9]ms, TR=2s, 3.2x3.2x3.2mm3, bandwidth=1532Hz/pix). Changes in $$$Ф_{0,ch}$$$ due to motion were investigated for three volunteers who rotated their head slowly but continuously about the left-right axis during the acquisition of dual-echo EPI. For one volunteer, additional dual-echo GE scans (with higher SNR and resolution than EPI) were acquired at 8 head poses with no motion during acquisition (TEs=[2.5,5.0]ms, TR=400ms, 1.6x1.6x2mm3, bandwidth=540Hz/pix).


Field-maps were calculated for all acquisitions using the Hermitian inner product8. These were multiplied by the first TE and subtracted from separate-channel phase data yielding $$$Ф_{0,ch}$$$ for all channels. GE scans were additionally used for evaluation of phase combination quality when $$$Ф_{0,ch}$$$ were acquired at a different pose than a target image (i.e. when motion occurred between the reference and the target scan). For this purpose combined complex data $$$C_{comb}^{t,r}$$$ were calculated according to6:


where t and r denote the target and reference pose respectively, ch is a channel index. When r≠t the $$$Ф_{0,ch}^r$$$ were extrapolated outside the brain to account for motion. The combined phase was obtained from $$$angle(C_{comb}^{t,r})$$$. Errors in the phase were mapped by taking the absolute value of the difference between phase reconstructed using $$$Ф_{0,ch}^r$$$ with r=t (optimal solution with no motion) and r≠t (non-optimal solution with motion). The quality Q of phase combination was quantified using6:



During a 40min long phantom experiment the $$$Ф_{0,ch}$$$ increased slowly but remained small: the weighted mean change in $$$Ф_{0,ch}$$$ (with separate magnitudes as weights) from the beginning to the end of the experiment was 0.061±0.017rad.

Figure 1 presents $$$Ф_{0,ch}$$$ changes in 4 representative channels from GE scans with head rotation up to 12.0°. The weighted mean change in $$$Ф_{0,ch}$$$ was up to 0.22±0.13rad for 12.0° rotation (Fig.1e, channel 16). Changes in $$$Ф_{0,ch}$$$ were low at all poses in the regions characterized by high signal (Fig.1d). Similar results, with the same range of motion (12.0°), were obtained for EPI measurements.

Figure 2 shows phase images combined using $$$Ф_0^r$$$ with r=t=6 or r=t=8 (Fig.2b) and r=1, t=6 or t=8 (Fig.2c). The difference between those two scenarios is presented in Fig.2d, where phase errors up to 0.3rad occurred in a dorsal slice for 6.3° rotation between reference and target scan (Fig.2d, Pose 6) and 0.6rad for 12° rotation (Fig.2d, Pose 8). Those errors can be translated into distortion correction errors of about 0.1 (for 6.3°) and 0.2 (for 12°) voxel for a sequence parameters typical for whole-brain fMRI at 7T (9,10) (Fig.2c, scale in voxels). The quality of phase matching was reduced by up to 2% for the largest head rotation (Fig.2e).

Discussion and conclusion

Long EPI measurement (40min) and large motions cause changes in separate-channel $$$Ф_{0,ch}$$$ (0.22±0.13rad for 12.0° rotation), which have little effect on the combined phase images. Negligible unwarping errors of about 0.2 voxel and reduction in phase matching quality by only 2% allow us to conclude that the assumption of $$$Ф_{0,ch}$$$ temporal stability holds and phase combination and dynamic distortion correction methods based on this assumption should work at 7T with separate channel-coils and substantial motion.


This study was funded by a DOC fellowship of the Austrian Academy of Science. Additional support was provided by the Austrian Science Fund (FWF KLI 264).


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Changes in $$$Ф_{0,ch}$$$ with head motion from GE acquisitions at pose 6 (c) and 8 (d). Plots (e) show that $$$Ф_{0,ch}$$$ change moderately as a function of head rotation. In regions with low signal expected phase errors (open-ended fringe lines) and increased $$$Ф_{0,ch}$$$ changes are apparent (see arrows).

The effect of motion-related $$$Ф_{0,ch}$$$-changes on phase combination. Phase images at pose 6 and 8 were combined using $$$Ф_{0,ch}$$$ from the corresponding pose (b) or from pose 1 (c). As the consequence of using $$$Ф_{0,ch}$$$ from pose 1 moderate phase errors (d) and phase matching quality reduction (e) are observed.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)